The Multi-view Geometry of Parallel Cylinders

In this paper we study structure from motion problems for parallel cylinders. Using sparse keypoint correspondences is an efficient (and standard) way to solve the structure from motion problem. However, point features are sometimes unavailable and they can be unstable over time and viewing conditions. Instead, we propose a framework based on silhouettes of quadric surfaces, with special emphasis on parallel cylinders. Such structures are quite common, e.g. trees, lampposts, pillars, and furniture legs. Traditionally, the projection of the center lines of such cylinders have been considered and used in computer vision. Here, we demonstrate that the apparent width of the cylinders also contains useful information for structure and motion estimation. We provide mathematical analysis of relative structure and relative motion tensors, which is used to develop a number of minimal solvers for simultaneously estimating camera pose and scene structure from silhouette lines of cylinders. These solvers can be used efficiently in robust estimation schemes, such as RANSAC. We use Sampson-approximation methods for efficient estimation using over-determined data and develop averaging techniques. We also perform synthetic accuracy and robustness tests and evaluate our methods on a number of real-world scenarios.